34 citations · 107 across the 25 of their papers we have counts for
26 papers
Dimension gap and phase transition for one-dimensional random walks with reflective boundary
Maik Gröger, Johannes Jaerisch, Marc Kesseböhmer
We study - and -extensions of interval maps with at most countably many full branches modelling one-dimensional random walks without and with a reflective bou…
Equality of Hölder exponents for distribution functions of Gibbs measures
Pieter Allaart, Johannes Jaerisch
Pointwise Hölder exponents describe the degree of regularity of a function near a point. For a function , a number and a point ,…
Amenable graphs and the spectral radius of extensions of Markov maps
Johannes Jaerisch, Elaine Rocha, Manuel Stadlbauer
We discuss relations between the amenability of a graph and spectral properties of a random walk driven by a dynamical system. In order to include graphs which are not locally comp…
Bowen's formula for a rational graph-directed Markov system
Tadashi Arimitsu, Johannes Jaerisch, Hiroki Sumi +1
We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating co…
Large deviations of homological growth rates for hyperbolic surfaces
Johannes Jaerisch, Hiroki Takahasi
We perform a large deviations analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. For surfaces uniformized by a wide class of Fuchsian groups of the…
Multifractal analysis of homological growth rates for hyperbolic surfaces
Johannes Jaerisch, Hiroki Takahasi
We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level…
Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
Johannes Jaerisch, Hiroki Takahasi
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the mixed mu…
Thermodynamic formalism for transient dynamics on the real line
Maik Gröger, Johannes Jaerisch, Marc Kesseböhmer
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic -extensions of expanding interval maps.…
Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line
Johannes Jaerisch, Hiroki Sumi
We refine the multifractal formalism for the local dimension of a Gibbs measure supported on the attractor of a conformal iterated functions system on the real line. Namely…
Spectral gap property for random dynamics on the real line and multifractal analysis of generalised Takagi functions
Johannes Jaerisch, Hiroki Sumi
We consider the random iteration of finitely many expanding diffeomorphisms on the real line without a common fixed point. We derive the spectral gap property o…
Weighted cogrowth formula for free groups
Johannes Jaerisch, Katsuhiko Matsuzaki
We investigate the relationship between geometric, analytic and probabilistic indices for quotients of the Cayley graph of the free group endowed with variable edg…
A multifractal analysis for cuspidal windings on hyperbolic surfaces
Johannes Jaerisch, Marc Kesseböhmer, Sara Munday
In this paper we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp winding number. We will comp…
Pointwise Hölder Exponents of the Complex Analogues of the Takagi Function in Random Complex Dynamics
Johannes Jaerisch, Hiroki Sumi
We investigate the Hölder regularity of the function of the probability of tending to one minimal set, the partial derivatives of with respect to the probability parameters…
Growth and cogrowth of normal subgroups of a free group
Johannes Jaerisch, Katsuhiko Matsuzaki
We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both, their growths tend to the upper bound and their cogrowths tend to…
Normalizer, divergence type and Patterson measure for discrete groups of the Gromov hyperbolic space
Katsuhiko Matsuzaki, Yasuhiro Yabuki, Johannes Jaerisch
For a non-elementary discrete isometry group of divergence type acting on a proper geodesic -hyperbolic space, we prove that its Patterson measure is quasi-invariant under t…
Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method
Johannes Jaerisch, Hiroki Sumi
We investigate the dynamics of semigroups of rational maps on the Riemann sphere. To establish a fractal theory of the Julia sets of infinitely generated semigroups of rational map…
Multifractal formalism for expanding rational semigroups and random complex dynamical systems
Johannes Jaerisch, Hiroki Sumi
We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analy…
Group Extended Markov Systems, Amenability, and the Perron-Frobenius Operator
Johannes Jaerisch
We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a…
Recurrence and pressure for group extensions
Johannes Jaerisch
We investigate the thermodynamic formalism for recurrent potentials on group extensions of countable Markov shifts. Our main result characterises recurrent potentials depending onl…
Conformal Fractals for Normal Subgroups of Free Groups
Johannes Jaerisch
We investigate subsets of a multifractal decomposition of the limit set of a conformal graph directed Markov system, which is constructed from the Cayley graph of a free group with…
A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups
Johannes Jaerisch
We give a short new proof that for each non-elementary Kleinian group , the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the e…
A Fréchet law and an Erdös-Philipp law for maximal cuspidal windings
Johannes Jaerisch, Marc Kesseböhmer, Bernd O. Stratmann
In this paper we establish a Fréchet law for maximal cuspidal windings of the geodesic flow on a Riemannian surface associated with an arbitrary finitely generated, essentially fre…
Fractal Models for Normal Subgroups of Schottky Groups
Johannes Jaerisch
For a normal subgroup of the free group $\F_d$ with at least two generators we introduce the radial limit set $\Lr(N,Φ)$ of with respect to a graph directed Markov system $…
Induced topological pressure for countable state Markov shifts
Johannes Jaerisch, Marc Kesseböhmer, Sanaz Lamei
We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. F…